While the above discoveries raise hopes for 2D spin devices for spintronics [1]}, [2]}, to realize such practical applications it is important to understand their thermal properties in detail. Thermal excitations in long-range ferromagnetic ordered materials appear as spin waves, or magnons as their quantized units. Given the structural similarity, the magnon band structures of honeycomb ferromagnets are expected to look analogous to the electronic band structure of graphene [3]}, [4]}. The latter is well known to exhibit linear energy-momentum relations (\(E\propto p\) ) near its Fermi energy, where conduction electrons behave as relativistic massless Dirac particles overcoming wave-particle duality [5]}. It was thus predicted that the bosonic version of Dirac particles, or Dirac magnons, should also appear on the magnon bands of honeycomb ferromagnets [4]}. Such linear magnon dispersion relations have experimentally been observed earlier in CrBr\(_3\)  [7]}, and more recently in CoTiO\(_3\)  [8]}, [9]} and a three dimensional antiferromagnet Cu\(_3\) TeO\(_6\)  [10]}, [11]}. In the spintronic transport, one of the key research interests lies in whether or not these Dirac magnons will be massive and thereby open an insulating gap in the bulk bands. If the bulk gap opens by breaking the time-reversal symmetry at the Dirac point, the accompanying edge states will be gapless allowing topological transport [12]}, [13]}. One of the best examples of such topological band structure is found in 2D graphene, where spin-orbit coupling opens a small electronic band gap (\(\sim \)  1 \(\mu \) eV) at its six-fold Dirac wave vectors, \(Q =(\frac{1}{3}, \frac{1}{3})\) . In the case of honeycomb ferromagnets, the antisymmetric Dzyaloshinkii-Moriya (DM) interactions between the next nearest neighbor spins may open topological energy gaps at the magnon Dirac points [14]}. The resultant magnon band structure will be separated into two, one higher and the other lower in energy, in which Berry curvatures are integrated to the integer Chern numbers \(C^{\pm }=\pm 1\) , respectively [15]}. Recently, finite energy gaps were indeed observed in the magnon bands of CrI\(_3\)  [16]}, [17]}, [18]} and CrBr\(_3\)  [19]}, respectively, indicating that the Dirac magnons in these ferromagnets are massive and topological.
